Ava is starting a cake-baking business, and she has just spent $150 for equipment. She figures that each cake will cost $4.50 to make, and she plans to sell her cakes for $12 each.Ava wants to find the number of cakes, c, she must sell to break even. In other words, she wants to know how many cakes she must sell before she has made as much money as she has spent. Which equation can she use?150+4.5c=12cc(150+4.5)=12c4.5c+12c=150150–4.5c=12c4.5c+150=12150c+4.5=12How many cakes must Ava sell before she has made as much money as she has spent?cakesSubmit
Question
Ava is starting a cake-baking business, and she has just spent 4.50 to make, and she plans to sell her cakes for $12 each.Ava wants to find the number of cakes, c, she must sell to break even. In other words, she wants to know how many cakes she must sell before she has made as much money as she has spent. Which equation can she use?150+4.5c=12cc(150+4.5)=12c4.5c+12c=150150–4.5c=12c4.5c+150=12150c+4.5=12How many cakes must Ava sell before she has made as much money as she has spent?cakesSubmit
Solution
The equation Ava can use to find out how many cakes she needs to sell to break even is 150 + 4.5c = 12c. This equation represents the total cost (initial cost of equipment + cost of making each cake) equals the total revenue (price of each cake times the number of cakes sold).
To find out how many cakes Ava must sell, we can solve the equation for c:
150 + 4.5c = 12c 150 = 12c - 4.5c 150 = 7.5c
Now, divide each side by 7.5 to solve for c:
150 / 7.5 = c c = 20
So, Ava must sell 20 cakes to break even.
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